The generalization of the Local Density Approximation (LDA) method for the systems with strong Coulomb correlations is presented which gives a correct description of the Mott insulators. The LDA+U method is based on the model hamiltonian approach and allows to take into account the non-sphericity of the Coulomb and exchange interactions. parameters. Orbital-dependent LDA+U potential gives correct orbital polarization and corresponding Jahn-Teller distortion. To calculate the spectra of the strongly correlated systems the impurity Anderson model should be solved with a many-electron trial wave function. All parameters of the many-electron hamiltonian are taken from LDA+U calculations. The method was applied to NiO and has shown good agreement with experimental photoemission spectra and with the oxygen Kα X-ray emission spectrum.

http://absimage.aps.org/image/MAR06/MWS_MAR06-2005-007233.pdf

First-principles calculations of electronic structure and spectra of strongly correlated systems: the LDA+U method

First-principles-based multiscale models are ever more successful in addressing the wide range of length and time scales over which material–function relationships evolve in heterogeneous catalysis. They provide invaluable mechanistic insight and allow screening of vast materials spaces for promising new catalysts — in silico and at predictive quality. Here, we briefly review methodological cornerstones of existing approaches and highlight successes and ongoing developments. The biggest challenge is to overcome presently largely static couplings between the descriptions at the various scales to adequately treat the dynamic and adaptive nature of working catalysts. On the road towards a higher structural, mechanistic and environmental complexity, it is, in particular, the fusion with machine learning methodology that promises rapid advances in the years to come. First-principles-based multiscale models provide mechanistic insight and allow screening of large materials spaces to find promising new catalysts. In this Review, Reuter and co-workers discuss methodological cornerstones of existing approaches and highlight successes and ongoing developments in the field.

First-principles-based multiscale modelling of heterogeneous catalysis

Climate change has prompted scientists to search for possible ways of reducing CO2 emissions or even capturing it from the atmosphere. Catalytic reduction of CO2 into value-added chemicals has been...

Photocatalytic CO [sub] 2 reduction : a review of ab initio mechanism, kinetics, and multiscale modeling simulations

Chemical kinetic modeling in heterogeneous catalysis is advancing in its ability to provide qualitatively or even quantitatively accurate prediction of real-world behavior because of new advances i...

Progress in Accurate Chemical Kinetic Modeling, Simulations, and Parameter Estimation for Heterogeneous Catalysis

This review article is intended as a practical guide for newcomers to the field of kinetic Monte Carlo (KMC) simulations, and specifically to lattice KMC simulations as prevalently used for surface and interface applications. We will provide worked out examples using the kmos code, where we highlight the central approximations made in implementing a KMC model as well as possible pitfalls. This includes the mapping of the problem onto a lattice and the derivation of rate constant expressions for various elementary processes. Example KMC models will be presented within the application areas surface diffusion, crystal growth and heterogeneous catalysis, covering both transient and steady-state kinetics as well as the preparation of various initial states of the system. We highlight the sensitivity of KMC models to the elementary processes included, as well as to possible errors in the rate constants. For catalysis models in particular, a recurrent challenge is the occurrence of processes at very different timescales, e.g., fast diffusion processes and slow chemical reactions. We demonstrate how to overcome this timescale disparity problem using recently developed acceleration algorithms. Finally, we will discuss how to account for lateral interactions between the species adsorbed to the lattice, which can play an important role in all application areas covered here.

/pdf/a-practical-guide-to-surface-kinetic-monte-carlo-simulations-2ggg0a9h0i.pdf

A Practical Guide to Surface Kinetic Monte Carlo Simulations

In the last decade, first-principles-based microkinetic modeling has been developed into an important tool for a mechanistic understanding of heterogeneous catalysis. A commonly known, but hitherto barely analyzed issue in this kind of modeling is the presence of sizable errors from the use of approximate Density Functional Theory (DFT). We here address the propagation of these errors to the catalytic turnover frequency (TOF) by global sensitivity and uncertainty analysis. Both analyses require the numerical quadrature of high-dimensional integrals. To achieve this efficiently, we utilize and extend an adaptive sparse grid approach and exploit the confinement of the strongly non-linear behavior of the TOF to local regions of the parameter space. We demonstrate the methodology on a model of the oxygen evolution reaction at the Co3O4 (110)-A surface, using a maximum entropy error model that imposes nothing but reasonable bounds on the errors. For this setting, the DFT errors lead to an absolute uncertainty of several orders of magnitude in the TOF. We nevertheless find that it is still possible to draw conclusions from such uncertain models about the atomistic aspects controlling the reactivity. A comparison with derivative-based local sensitivity analysis instead reveals that this more established approach provides incomplete information. Since the adaptive sparse grids allow for the evaluation of the integrals with only a modest number of function evaluations, this approach opens the way for a global sensitivity analysis of more complex models, for instance, models based on kinetic Monte Carlo simulations.

Addressing global uncertainty and sensitivity in first-principles based microkinetic models by an adaptive sparse grid approach.

Error propagation in first-principles kinetic Monte Carlo simulation

Gaining insights into the working principles of photocatalysts on an atomic scale is a challenging task The obviously high complexity of the reaction mechanism involving photoexcited electrons and

/pdf/field-heterogeneities-and-their-impact-on-photocatalysis-2yn3zm6zrc.pdf

Field Heterogeneities and Their Impact on Photocatalysis: Combining Optical and Kinetic Monte Carlo Simulations on the Nanoscale

Many problems require to approximate an expected value by some kind of Monte Carlo (MC) sampling, e.g. molecular dynamics (MD) or simulation of stochastic reaction models (also termed kinetic Monte Carlo (kMC)). Often, we are furthermore interested in some integral of the MC model's output over the input parameters. We present a Multilevel Adaptive Sparse Grid strategy for the numerical integration of such problems where the integrand is implicitly defined by a Monte Carlo model. In this approach, we exploit different levels of sampling accuracy in the Monte Carlo model to reduce the overall computational costs compared to a single level approach. Unlike existing approaches for Multilevel Numerical Quadrature, our approach is not based on a telescoping sum, but we rather utilize the intrinsic multilevel structure of the sparse grids and the employed locally supported, piecewise linear basis functions. Besides illustrative toy models, we demonstrate the methodology on a realistic kMC model for CO oxidation. We find significant savings compared to the single level approach - often orders of magnitude.

Sandra Döpking

Papers

Addressing global uncertainty and sensitivity in first-principles based microkinetic models by an adaptive sparse grid approach.

Error propagation in first-principles kinetic Monte Carlo simulation

Field Heterogeneities and Their Impact on Photocatalysis: Combining Optical and Kinetic Monte Carlo Simulations on the Nanoscale

Multilevel Adaptive Sparse Grid Quadrature for Monte Carlo models